It also requires the vehicle to be superlocked to make it 'lazy unlock' and move the seats to either memory 1 or 2 if they are fitted.
I have a fob tester that captures the code the key is sending out and from that I can work out what key # it is - but I'm away at the moment, so not home to be able to use it...
The red light on the fob when you put it in the ignition is the passive immobilisation circuit working to get the fob to send the unlock code to the BECM to turn off the immobiliser. The fact that you get this on one fob and then can start the vehicle says to me that the receiver is all working OK - maybe the antenna has been disconnected so the range is reduced though.
My thoughts... maybe the second fob that doesn't flash the red light has a faulty pickup coil, so it's not being triggered by the ignition to send an unlock code. I've heard of a few instances where people have opened up the key fob casings to replace the casing, or repair switches, where they've found the pickup coil component loose/not attached to the PCB. If you don't get the red light flashing when you press either of the buttons, then I'd be checking the battery contacts in the fob and things like that too.
You should be able to sync the keys in the door - yes.. If this isn't happening, then I would first see if the receiver has the antenna connected. There should still be enough range without it connected to get communication, but if there is RF interference around then maybe the signal isn't getting through properly.
If still no joy, then I would also test the microswitches in the drivers door, as these can affect the BECM recognising the key being turned in the door, and if it's not recognising the key being turned, then it might also be messing with the sync procedure. The fact that one of the fobs will sync in the ignition, but not the door, and the other one won't sync at all suggests to me there are more than one problem... one possibly being the door latch if neither will sync in the door, and another problem with the second fob not being triggered by the passive coil around the ignition.
I would be able to be certain without actually seeing the vehicle/hooking it up - but that's my thought process from what I've read